Last and shoe grading



Feb. 27, TOPHAM LAST AND SHOE GRADING Filed March 15; 1930 ball.

is and 9 inches in perimeter.

Patented Feb. 27, 1934 UNITED STATES PATENT OFFICE LAST AND SHOE GRADING Application March 15, 1930. Serial No. 436,197

5 Claims.

This invention relates to the manufacture of lasts and shoes.

Heretofore it has been the custom to grade lasts and shoes arithmetically, that is, by equal increments per unit of increase in nominal length and width. These increments are, in size grading, inch in length, as measured on the sizestick, and inch in perimeter at the ball, as measured by a tape around that part of the forepart known as the ball, per unit increase in length; and in width grading, inch in perimeter at the ball per unit increase in width. For example, the standard 7C last is inches long on the size-stick, and is 8 inches in perimeter at the The 8G of this model is 10% inches long and 8% inches in perimeter; the 100 is 11- inches long and 9%, inches in perimeter, and so on: while the 7D is 10% inches long and 8%, inches in perimeter, and the 7F, 10 inches long In short, the sizestick length of any last of the standard dimensions will be 10% inches plus inch times the algebraic difference between its length number and '7; while its perimeter at the ball will be 8% inches plus inch times the algebraic sum of the algebraic differences between its length and width numbers and those of the 7C respectively. It should be noted that the nominal width of a last defines no dimension of it; it indicates only some relation between the length and the girth.

This system has the advantage that in testing the product of a last lathe or in ascertaining the length and girth of a given last, a single sizestick, or caliper, graduated in inch units, and

75 a single tape, graduated in inch units (in actual practice an ordinary tape, graduated in inch units) can be used to check or ascertain the dimensions of any last whatever and its relations to a model from which it was cut. The system is, however, subject to serious disadvantages, which will appear from the following discussion.

A little computation will show that all lasts of a series (or set of the same style) of the same 5 nominal width are nearly geometrically similar solids, but that the magnification factors necessary to produce them from one another in turn are not equal. For example, the length magniiication factor necessary to produce a standard 0 8 from a '7 is 131/127=1.0315; to produce a 9 from an 8 is 135/131=1.0305; to produce a 10 from a 9 is 139/135=1.0296, and so on. The variation in the grading factor in shoemaking generally, however, is really much greater than this because of variations in actual length of lasts of the same nominal length due to varying styles. A 70 model will measure anywhere from 7 to 11 on the size-stick, depending on its style; that is, it may be anywhere from 10, inches to 11% inches in length. The length magnification factors necessary to produce an 80 from two such models are l3l/127:l.03l5 and 147/143: 1.0280 respectively, which requires adjustments of the length grading apparatus differing by 10% of themselves, since the movement of the adjustment pointer of a last lathe grading mechanism is a measure of the difference of the grading factor from unity.

This results, furthermore, in a practical disadvantage in shoemaking and shoe fitting. All of these 70 last models of varying styles and absolute lengths are substantially alike from the heel to the ball, that is, over the foot fitting part of the last. Since a short 70 last is graded more rapidly than a long 7C last, in order to produce the inch increment per length unit, the absolute length of the heel-ball portion of a short 8C will be greater than that of a long 80. Consequently shoes of the same nominal size but of different styles will fit differently; furthermore, in such a machine as the automatic leveling machine where the length of the travel and the tip f the leveling roll are regulated by the position of the ball line, the machine should be set differently for a long style than for a short when treating shoes other than the model size.

It will thus be clear that when operating a last lathe equipped with a simple length grader the same settings of the apparatus cannot be used, according to the system used heretofore, in grading from two models of the same nominal length but of different actual lengths. The actual length grading apparatus used in the last lathe comprises a swinging lever having a sliding pivotal connection with a fixed pivot in the frame, a fixed pivot on the model wheel carriage, and a pivotal connection with the cutter carriage which is adjustable along the lever to positions on either side of the second-named true of the pivot to establish the grading ratio or factor. It has been attempted to obviate the difiiculty inherent in the necessity of varying grading factors by making the pivot in the machine frame adjustable along the lever, thus changing the advantage of the lever to make it correspond to the same setting scale for all models, but this scheme has not been practically successful since an accurate adjustment of the lower pivot is more trouble than the operator is willing to take, and an approximate adjustment does not materially diminish the amount of empirical trial necessary to produce a last of the proper length. The proper position of the pointer on the adjustment scale is thus practically always found by trial and consequent waste of a number of blocks and considerable time.

The above discussion has been based on the 7C model alone, but the range in length from childrens to mens work necessitates the use, in producing all the lasts required in shoe making, of models which vary between far wider limits than those indicated; so that the real difficulty is much worse than the figures given above would indicate.

The difiiculty in width grading is exactly similar, due to the great variation in perimeters of the models used for the different lines of work, from childrens to mens lasts. In the case of the wid h grading mechanism of the last lathe there is no way at all of even reasonably approximately taking care of the difficulty, and the width grader setting is utterly empirical in most cases.

In grading shoe upper patterns in the pattern grading machine the same difficulty is met, and is dealt with by the provision of about setting scales which are interchangeably mounted in the machine to correspond to different kinds of work, and even then a considerable amount of experimentation is necessary. This scheme is prohibitively troublesome in the last lathe and has never been adopted.

It is a principal object of the present invention to obviate all these difficulties, and I have found that this can be accomplished by grading lasts and shoes geometrically, as distinguished from arithmetically, as in the system heretofore in use. By geometric grading is meant that successive members of a series of graded objects vary by a uniform percentage of a given characteristic, from one to another, instead of by a uniform absolute amount, from one to another. Thus the grading factors in producing a last of any given nominal length and width from a model of any style will always be the same, regardless of the actual length and girth of the model, and a single grading scale can be readily provided for each grading mechanism and used for all work, strictly in accordance with its own indicia; that is, the graduation marks on it will mean exactly what they say as regards nominal increases in size and girth, irrespective of the model in the machine, and the same is graduation marks of the corresponding single size-stick and tape used to check the work of the machine or to ascertain the size and width characteristics of any given last relatively to its model. This avoids the waste of time and material due to the necessity of cutting and trying under the present system. The machine will produce the desired result at the first trial, and the relation of the length and girth of the last produced to those of the model used can be ascertained by using one last stick and one tape,

irrespective of what the length and girth of the model were.

It should be noticed that the grading system provided by this invention is not merely equivalent to the acceptance of a different desideratum as to the relations between the lasts of a set. It is of course possible to set the length and width graders of the ordinary last lathe two sizes up, for example, by the scales provided with the machine, and to call the last produced two sizes longer than the model and of the same nominal width. This procedure would not secure all the advantages of the present invention because the problem of ascertaining the relations of such lasts to the models from which they were graded would entail hopeless confusion. Suppose, for example, that the machine were built to grade inch increments in length per size from a standard 76 model, as described above. A tape and last stick can be constructed, with their graduations corresponding to the dimensions of the successive lasts produced from this model by the machine, but these will not Work in connection with a shorter or longer model and the lasts generated from it in this machine. For example, with such a machine the 40 would be 1 inch shorter than the 76; its length grading factor would be 115/127, and inversely the would be 127/115 as long as the 4C: and if the machine were set to grade three sizes up, the would be 139/127 as long as the 70. But if this 40 last were put in the machine as a womens model and a 7G graded from it by setting the graders up three sizes from the zero mark the 70 produced would be 139/127, instead of 127/115, as long as the 40 model. If this 40 model and 7C last thus graded from it were placed on the size-stick constructed as stated above, the graduation marks measuring their lengths would not be three sizes apart on the stick. Thus a distinct stick and tape would have to be made for every length and girth of model used. With the present invention, a last three sizes longer or wider than a model will always be longer or wider than the model by the same percentage of the model length I,

or girth, and. the measurement of the model and the last on the same stick and tape will always show the same graduational differences.

The practice just described of using the present machine would sacrifice the advantage of using the same measuring apparatus for all work which is found in the system used heretofore, for the advantage of economy of material in which the old system is lacking. The present invention preserves the former advantage and secures the latter.

Another advantage of thepresent invention is that the foot fitting portions of lasts of all styles Will be graded alike since the grading factors are constant for all styles.

In the proposed system the large objects difier more from one another in absolute dimensions than do the small ones, since the uniform percentage is taken on a larger quantity among the large objects than among the small. stitutes another advantage of the invention, since it is not advisable to grade large objects in such small absolute intervals as in the case of small objects.

Any disadvantage which might result from this characteristic of the system under special conditions (for example, if it is desired to grade childrens shoes on a larger percentage than mens,

as childrens feet are growing), can be avoided This coni by making the constant percentage upon which the system is based a submultiple of the different percentages desired throughout the whole range, and using a larger multiple of it inthe smaller lasts than in the larger. This will of course require more care on the part of the operator (unless exactly the same scheme of multiples is adopted for all classes of work), but the inherent advantages of always setting the machine exactly on the same definite mark and of using a single measuring apparatus are retained, and this is something that has never been accomplished in last making or pattern making in all classes of work.

The drawing shows the profiles of a series of six lasts marked a to f illustrating the invention. To avoid confusion of the lines of the drawing the lasts illustrated are two sizes apart, and their shank portions are not separately drawn. The grade used is 3% per size: that is, each last illustrated is (1.03) as large in length and girth as its next smaller predecessor on the drawing. (1.03 is a rough average of the grades heretofore used in mens work.) The outlines of the six lasts are formed with lines of difierent types of discontinuity to make them recognizable.

These lasts are shown as resting on a line 10 which corresponds to the size-stick, in the positions in which their lengths are measured on that instrument. Their toes are shown abutting on a line 12 which corresponds to the fixed abutment of the size-stick, and their heel ends are shown as abutting on lines 14a to 14: which correspond to the movable abutment of the size-stick in its diiierent positions. The spacing of these lines 151 illustrates the geometric characteristic of the grade. An ordinary set of lasts thus shown would cause the lines 14 to be equally spaced.

Any one of the lasts shown can be regarded as a model, and any one of the others graded from it in a last lathe provided with geometric setting scales, by merely setting the graders the proper number of graduation marks up or down from the neutral mark which corresponds to 1:1 reproduction, and a single geometrically graduated size-stick and tape will enable any two of them to be directly compared. It must be understood that each last in this set is (1.03) as long as its next shorter neighbor. The last marked a being taken as the model, the last marked b is metic geometric 3O 9. 250 9. 403 +0153 9. 917 9. 976 +0. 059 7 O 10. 583 10. 583 0. 000 9G 11. 250 11. 228 -0. 022 110 11.917 11. 912 -0. 005 13G 12. 583 12. 037 +0. 054

The differences in the last column are not very u significant as regards fit, except for the 3C which is about size too long, but any such discrepancies, except that of the 11C, would heretofore entail rejection of the last in the last factory. The two systems are therefore essentially different.

Many grading systems having the herein-described geometrical characteristics may be developed, according to the practical manufacturing conditions that may exist. Suppose, for example, that we are given the problem of developing a set of lasts corresponding as closely as possible to the run of mens lasts from 5 to 11, and in widths A to E of the ordinary system.

The lengths and girths of these lasts in the arithmetic system are given below, assuming the lengths to be the same in all widths.

Table A-Lengths Table B-Girths No. Size Girth Weight H m w 1 7. 5 1 2 7. 625 l 3 7. 2 4 7. 875 2 5 8. 000 3 6 8.125 3 7 8. 25 i 8 8. 375 4 9 8.5 5 l0 8. 625 5 11 8. 75 5 12 i I n. 8. 875 5 13 1013, 0C, 8D, 7E.. 0.000 5 14 10%13, 0%0, 8%1), UQE 0.125 4 15 11B, 106, 9D, 8E 9. 25 4 10 10% 9. 375 3 17 ll 3 l8 2 19 2 20 l 21 l In order to secure the best correspondence between the two systems we will treat the length and girth problems independently. Taking the length problem first, we desire to find a length, L, for the #5 last, and a size grad'ng factor, G,

such that, as closely as possible, the following equations will be satisfied:

No. Equation 1 L 9. 9167 2 LG =10. 0833 (G) 3 LG=10. 25

etc. 13

this is to put the Equations (C) into logarithmic form. Let w=log L and y=log G. Then the Equations (C) become No. 1 1 0. 99637=0 2 z+y1.00360=0 (D) 3 x+2g 1. 01072= 0 etc. 13 I z-l-IZy-l. 07616=O which are linear in x, y. If the y'th equation of (D) be Written in the form a x+b y+n =0 (E) where a, b, and n are the numerical coeificients the two normal equations giving the best values of x and y are where [all] :sum of the 13 products aa, [ab] sum of the 13 products ab, and so on.

These normal equations, when thus formed, are

which give The lengths of the lasts are given in the following table in the column marked Lg. The column marked L -La gives the differences between the geometrically graded lengths and the arithmetically, or standard, graded lengths.

l 5 9.9430 +.0263 2 5% 10.0963 +.0l30 3 6 10.2520 +.O020 4 6% 10.4100 .0067 5 7 10.57 -.0128 6 7% 10.7334 .0166 7 8 10.8989 -.0177 S 8% 11.0669 .0l04 9 9 11.2375 .0125 10 9% 11.4107 .0060 11 10 11.5866 +.0033 12 10% 11.7652 +.O152 13 11 11.9466 +.0299

In solving the corresponding problem relative to the girths it is necessary to remember that the same numerical conditions arise from different numbers of lasts of the set (given in the Weight column in (B) the 5A girth comes in only once, while the 9A girth (since it is-the same as that of the 8B, 7C,.6D and 5E) comes in five times. There are equations in all, and they must all be used as if they were all really different, in order to get the best solution for, the system as a whole. There were 65 equations in the length problem, too, but they all entered five times each, so that it was necessary to use only the 13 different ones.

The normal equations formed as above from the 65 girth conditions are, if 10 is the logarithm of P, the girth of the 5A, and z is the logarithm of the half-size girth grading factor, G;

whence w=0.878' 77 P.=7.5642 2:0.0062261 G=1.01444 As pointed out above all these lasts have the advantage inherent in the old system, that they can be checked and their relations to one another ascertained, by means of a single size-stick and tape, the former built on a grade of (1.0l542) =1.03l()8 per size and the latter on a grade of 1.01444) =1.02909 per size.

without previous trial.

If it be desired, the length and width aspects of the abovedescribed problem may be combined, and the same grading factor obtained for both length and girth. There are then three unknowns to find, the length and the girth of the smallest last, and the common grading factor, and three normal equations will be found from the 130 fundamental equations. The system of geometrically graded dimensions which will best correspond to any given system can be found in this way.

Another advantage of the geometric system relates to the adjustment of shoe machinery for different sizes. In this system, if the length grading factor per size is, say, 1.03 (or in ordinary words, if we are using a 3% grade), the distance from the heel to the ball of all lasts of the same nominal length graded from size 7 models will be always the same, irrespective of style, since this distance in the 7s of all styles is always substantially the same, and is increased 3% of itself in making the size Bs. question of adjusting shoe machinery for different sizes is simplified, for example, in the leveling machine adjustment discussed above.

The set of lasts provided by the present invention can thus be cut on a last lathe provided with length and Width grader setting scales the adjustment can be always set and material.

exactly on these marks to produce the required lasts, with no Thus the acteristic. Other such characteristics may or may not so vary, in the series.

Having described my invention, what I claim as new and desire to secure by Letters Patent of the United States is:

1. That improvement in manufacturing lasts which consists in generating from a given model irrespective of its style or dimensions a series of lasts having a progressively varying dimensional characteristic, by making the ratios of the numerical values of said characteristic in each two successive lasts of the series all equal to the same number irrespective of the dimensions of the model.

2. That improvement in manufacturing lasts which consists in generating from a given model irrespective of its style or dimensions a series of lasts having a progressively varying dimensional characteristic, by making each of the ratios of the numerical values of said characteristic in each two successive lasts of the series an integral power of the same fundamental number throughout the series irrespective of the dimensions of the model.

3. That improvement in methods of manufacturing lasts which consists in generating from a given model irrespective of its style or dimensions a last having a given dimensional characteristic of the same numerical value as that of the corresponding dimensional characteristic of the model, generating from the said model a last differing from the model in the numerical value of the said characteristic by a given percentage of the numerical value of the said characteristic of the model, and generating from the said model a last differing from the last secondly referred to in the numerical value of the said characteristic by the same said percentage of its numerical value in the last secondly referred to, irrespective of the dimensions of the model.

4. That improvement in methods of manufacturing lasts which consists in generating from a given model irrespective of its style or dimensions a last having a given dimensional characteristic of the same numerical value as that of the corresponding dimensional characteristic of the model, generating from the said model a last differing from the model in the numerical value of the said characteristic by a given percentage of the numerical value of the said characteristic of the model, and generating from the said model the remaining members of a series of lasts each differing from its predecessor in the numerical value of the said characteristic, by the same said percentage of the numerical value of that characteristic in the predecessor, irrespective of the dimensions of the model.

5. That improvement in methods of manufacturing a set of lasts of the same style having a progressively varying dimensional characteristic, which consists in pantographically generating each of such lasts in a copy turning machine from a model and utilizing in each different case a magnification factor which is a different integral power of one fundamental number to effeet the said progressive variation of the said characteristic throughout the set, irrespective of the dimensions of the model.

LAURENCE E. TOPHAM. 

